Conic sections Flashcards

(30 cards)

1
Q

What are the four types of conic sections?

A

Circle, ellipse, parabola, hyperbola.

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2
Q

True or False: A circle is a type of ellipse.

A

True.

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3
Q

Fill in the blank: A parabola opens either _____ or _____.

A

upward, downward.

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4
Q

What is the standard form equation of a circle with center (h, k) and radius r?

A

(x - h)² + (y - k)² = r².

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5
Q

What is the general form of the equation of an ellipse?

A

(x²/a²) + (y²/b²) = 1.

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6
Q

Identify the conic section: x² + y² - 4x - 6y + 9 = 0.

A

Circle.

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7
Q

What is the definition of a hyperbola?

A

A set of points where the difference of the distances to two foci is constant.

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8
Q

True or False: The foci of a hyperbola are located along the transverse axis.

A

True.

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9
Q

What is the equation of a horizontal hyperbola?

A

(x²/a²) - (y²/b²) = 1.

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10
Q

Short answer: What is the directrix of a parabola?

A

A fixed line used in the definition of a parabola.

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11
Q

Fill in the blank: The major axis of an ellipse is the longest diameter that passes through the _____ and _____.

A

foci, center.

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12
Q

What is the eccentricity of a circle?

A

0.

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13
Q

Identify the conic section described: A set of all points in a plane equidistant from a point and a line.

A

Parabola.

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14
Q

What is the standard form of the equation for a vertical ellipse?

A

(x²/b²) + (y²/a²) = 1.

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15
Q

True or False: The vertices of a hyperbola are located at the endpoints of the conjugate axis.

A

False.

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16
Q

What do the terms ‘focus’ and ‘directrix’ relate to in conic sections?

A

They define the shape of conics, particularly parabolas.

17
Q

What is the difference between a major axis and a minor axis in an ellipse?

A

The major axis is longer than the minor axis.

18
Q

Fill in the blank: The distance between the foci of a hyperbola is _____ than the distance between the vertices.

19
Q

What is the standard form of a parabola that opens to the right?

A

(y - k)² = 4p(x - h).

20
Q

Identify the conic section: x² - 4y² = 16.

21
Q

What is the formula for eccentricity (e) of an ellipse?

A

e = c/a, where c is the distance from the center to a focus.

22
Q

True or False: All conic sections can be represented by second-degree polynomial equations.

23
Q

What does the term ‘latus rectum’ refer to in a parabola?

A

The line segment perpendicular to the axis of symmetry, passing through the focus.

24
Q

Fill in the blank: The foci of an ellipse are located _____ the center.

25
What is the relationship between the axes of symmetry in a hyperbola?
They are perpendicular to each other.
26
Identify the conic section: 9x² + 16y² = 144.
Ellipse.
27
What is the equation of a vertical hyperbola?
(y²/a²) - (x²/b²) = 1.
28
True or False: The vertices of a parabola are located at the focus.
False.
29
Fill in the blank: The center of a hyperbola is the midpoint between the _____ and _____.
foci, vertices.
30
What is the standard form of the equation for an ellipse with a vertical major axis?
(y - k)²/a² + (x - h)²/b² = 1.